Innovation, Diffusion and Trade: Theory and Measurement

Innovation, Diffusion and Trade: Theory and Measurement∗ Ana-Maria Santacreu

Abstract In the last decade, some countries in Asia and Europe grew much faster than average, and experienced a significant increase in the variety of goods that they import. A well known stylized fact is the existence of a positive correlation between trade and growth across countries. However, the mechanisms by which these two variables are connected are not well understood. I propose a general equilibrium model of innovation and international diffusion to analyse these connections. Technological progress drives growth and technology is embodied in new goods, which diffuse internationally through trade. The model is analysed outside the steady state, to capture differences in growth rates across countries. Using disaggregated trade data, and data on R&D, and output growth, I estimate the parameters of innovation and diffusion with Bayesian techniques. Finally, I carry out counterfactual analysis to examine the connections between trade and growth by changing various exogenous parameters. A 50% permanent decrease in the barriers to technology adoption in Asia increases world growth rates by around 1%. In the transition, Asia imports and grows faster than the rest of the world. A 50% permanent increase in the innovation productivity in Asia increases world growth rates by 3%. The higher productivity in Asia increases the demand for imports from the rest of the world. Either change leads simultaneously to both higher growth and more trade. ∗

I am very grateful to Jonathan Eaton for his support and guidance. I am also grateful to

Francisco Alcala, Diego Comin, Ana Cecilia Fieler, Mark Gertler, Boyan Jovanovic, Tobias Pfutze, Demian Pouzo, Kim Ruhl and Gianluca Violante for useful comments.

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1

Introduction

A well known stylized fact in the development literature is the existence of a positive correlation between trade and growth across countries. Economies that grow faster tend to trade more. If we decompose the increase in the trade to GDP ratio in the last decade, we observe that, for the average country, about 80% of this increase has been driven by the extensive margin (number of new varieties traded), while only 20% has been driven by the intensive margin (how much of each variety is traded). Thus, looking at the extensive margin of trade seems important to understand the recent development of several economies.1 In the last decade, some countries in Asia and Europe, such as China, India, and Ireland, grew much faster than average, and experienced a significant increase in the number of varieties that they imported.2 Motivated by the empirical evidence, recent studies have emphasized the impact that imports in new goods have in explaining productivity growth around the world. However, the mechanisms by which trade and growth are connected are still not well understood. I propose a multicountry model in which shocks to innovation and adoption can explain the mechanisms behind the connections that we observe in the data. The model is developed in a general equilibrium framework, with trade and growth being outcomes of the equilibrium. In the model, technology rather than factor accumulation, drives growth.3 Coun1

These results were obtained for a sample of 73 countries by Broda, Greenfield, and Weinstein

(2008). When they focus on developing countries, the effect of the extensive margin is even higher. Hummels and Klenow (2002) also perform this decomposition for exports and they find that the extensive margin explains two thirds of the increase in trade. 2 Santacreu (2006) obtains that more than 60% of the economic growth in Ireland in the last decade can be explained by an increase in the variety of goods that it imports from very innovative countries in the OECD. 3 See Parente and Prescott (1994) and Eaton and Kortum (2007), and Easterly and Levine (2001). There has been an extensive literature trying to identify whether differences in growth rates are driven mainly by factor accumulation (capital, in particular) or by TFP differences. An example is Young (1991). As a response to this literature, Easterly and Levine (2001) and Klenow and Rodriguez-Clare (2005) show that it is differences in TFP that drive differences in growth rates across countries. Even though capital a ccumulation has been important in several Asian economies, TFP growth affects the marginal rate of capital and it could explain why the rental rate of capital was so high in these countries.

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tries invest resources in R&D to create new technologies. Thus, technology is embodied in new intermediate goods, and countries may benefit from foreign innovations by importing the goods that embodied the technology. In each economy, there is a final sector that produces a non-traded good, using traded intermediate products according to a constant elasticity of substitution function. There is love-for-variety, in the sense that, keeping expenditure constant, more intermediate imputes generate more final output. New technologies are introduced in a country by investing resources in innovation. Innovators then sell the right to use the technology to a monopolistic competitive intermediate firm, for a specific transfer price. Finally, an adoption sector invests resources to make the good usable by final producers. A novel element of my framework is the fact that innovation and adoption are both endogenous processes. This introduces a trade-off by which countries decide how many resources to allocate to one activity or the other. This decision depends on the stage of development, and country-specific parameters. Models of growth based on innovation and technology transfer face the problem that there are no good measures of diffusion. The trade literature has filled this gap, using imports as an indirect measure.4 However, studies that quantify the impact of imports on growth are based on regression analysis that suffer endogeneity problems, since these two variables are both equilibrium outcomes.5 A recent attempt to give a more structural approach is the paper by Broda, Greenfield, and Weinstein (2008), who analyse the impact of trade in new and improved varieties on TFP growth for a large sample of countries. Although they provide a good measure of trade in varieties, their model is too stylized to make precise statements about the channels of growth. My paper constitutes an attempt to structurally analyse and quantify the mechanisms behind the connections between trade and growth. International diffusion implies that, in steady state, all countries grow at the same rate, while barriers to technology adoption create persistent income differences across countries.6 So far, models of innovation and diffusion have been analysed in steady state, restricting their attention to explaining differences in income per capita across countries. To analyse differences in growth rates, however, we need to look at the 4

See Keller (2004) for a survey of models that use imports to measure diffusion. Coe, Helpman, and Hoffmaister (1997) and Keller (1998) are good examples. 6 See Parente and Prescott (1994). 5

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transition. In this paper, I go one step further and solve for the transitional dynamics of the model. This allows me to account for the experience of countries such as China or India, which have been growing faster than average but are likely to share the same world growth rates in the long-run. The model is fitted to thirty-seven countries that are grouped, for tractability, into five regions: Asia, Eastern Europe, Western Europe, Japan, and the US. I use disaggregated trade data, data on a measure of the fraction of workers allocated to R&D, and output growth to estimate the parameters that govern innovation and diffusion with Bayesian techniques. I then decompose the sources of productivity growth in each region. The results show that almost 90% of productivity growth in Asia can be explained by innovations from the US and Japan. These two regions are also the main sources of foreign technology for other regions of the model. Technology transfer through trade of foreign innovations arises as an important source of productivity growth for countries lagging behind the technology frontier; domestic innovation has been the main source of growth for economies that are closer to the frontier.7 Finally, using counterfactuals I examine the connections between trade and growth by changing various exogenous parameters. A 50% permanent decrease in the barriers to technology adoption in Asia increases world growth rates by 1%; in the transition to the new steady state, trade rises, while Asia grows faster than the rest of the world. A 50% permanent increase in the innovation productivity in Asia increases world growth rates by 3%. The higher productivity in Asia increases the demand of imports from the rest of the world. Both changes induce a positive correlation between trade and growth. The rest of the paper is organized as follows. Section 2 presents the related literature. In section 3 I examine the data. In section 4, I present the model. Section 5 solves for the steady state. The model is estimated in section 6 and I present a decomposition of the growth rate of each country into the contribution of own and foreign innovation in section 7. In section 8, I compute the speed of convergence predicted 7

Cameron, Proudman, and Redding (2005) analyse a model for a panel of UK manufacturing

industries, in which innovation and technology transfer are the main sources of productivity growth for countries lagging behind the technology frontier. They find that technology transfer through international trade is the main driving source of growth for these countries. They obtain a positive and statistically significant effect of distance with respect to the frontier on productivity growth.

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by the model. I perform counterfactuals in sections 9. Section 10 concludes.

2

Related Literature

The paper builds on several streams of literature: First, the literature on endogenous growth in which technology is embodied in new goods. Technological progress is driven by the introduction of new types of intermediate products through innovation, as in Romer (1987) Second, the model relates to the literature on innovation and technology diffusion. The theoretical model is inspired in the work of Eaton and Kortum (1996) and Eaton and Kortum (1999a). Keller (2004) surveys the empirics of the effects of international diffusion on productivity. The lack of direct measures that can exploit the bilateral nature of adoption have led some economists to use indirect measures, such as trade in intermediate goods ( Rivera-Batiz and Romer (1991), Eaton and Kortum (2001), and Eaton and Kortum (2002)).8 Countries benefit from technologies developed elsewhere by importing the products that embody the technology. Coe, Helpman, and Hoffmaister (1997) study empirically the role of trade as a measure of diffusion. They find that total factor productivity in a panel of seventy-one developing countries is significantly related to the stock of R&D carried out by trading partners. In their analysis, trade, particularly the imports of machinery and equipment, facilitates the diffusion of knowledge. My model complements this literature by explicitly modeling the mechanisms that explain how trade and growth are connected. The paper also relates to the literature of trade in varieties. A variety is defined as a 6-digit category product from a particular source-country, reflecting the Armington assumption that products differ according to their source. It is important to note that the Armington assumption implies that each country produces a different variety. Therefore, a country that imports a good can never learn to produce, exactly, that good itself. To measure growth in imported varieties, I follow the methodology developed by Feenstra (1994) and adapted by Broda and Weinstein (2006) and Broda, Greenfield, and Weinstein (2008). In a recent paper, Broda, Greenfield, and 8

Comin and Hobijn (2004) provide direct measures of adoption for a large sample of countries and a large sample period; they do not distinguish, however, between technologies created in the country and those from abroad.

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Weinstein (2008) estimate the effects of trade on productivity growth. They find that trade in imported varieties accounts for 20% of TFP growth in the typical developing country and only 5% in the typical developed country. My paper follows Broda, Greenfield, and Weinstein (2008) to measure growth in varieties but differs in that I model explicitly the incentives of the different agents in the economy to undertake either research or adoption. Finally, and in contrast to previous studies in the literature, I model technology diffusion as an endogenous process: firms need to undertake a costly investment to be able to import a good. The incentives for the importer differ across sources and depend on the value of adopting a new technology. I adapt the approach in Comin and Gertler (2006) and Comin, Gertler, and Santacreu (2008) to an open economy setting. Further empirical evidence that shows that innovations are not transferred to other locations at a negligible cost can be found in Griliches (1957) and Teece (1977).

3

A Look at the Data

This section presents data on innovation, trade, and productivity for a sample of 37 countries. Based on these data, we can divide the world in three groups of countries: first, innovative economies in Europe, Japan, and the US, which grow and import at lower rates; second, less innovative countries in Europe and Asia, which grow and trade more than average; third, less developed countries in Africa and Latin America, which do not invest either in innovating or in adopting foreign innovations.

3.1

Trade and Productivity Growth

In the last decade, some countries in Asia and Europe have experienced a significant increase in the variety of goods that they import from the rest of the world. These countries have also been growing faster than average.9 Figure 1 shows, for a sample of thirty-seven countries, that there is a positive correlation between the average growth 9

One could argue that looking at exports is just as important as looking at imports to explain the development experienced by Asia and Eastern Europe. When I look at the growth in exported varieties and I compute the correlation with productivity growth, I obtain a correlation of 0.4. The correlation between productivity growth and growth in imports is almost 0.8.

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rate of income per capita and the expansion in import variety.10 I use bilateral trade data at the 6 digit level of disaggregation, from UN COMTRADE. A variaty is defined as a 6-digit product from a specific source of exports. Growth in imported varieties is computed as in Broda, Greenfield, and Weinstein (2008), who adjust for quality and symmetry bias. Output growth is growth in real GDP per capita, PPP adjusted, from World development Indicators in the World Bank. At the same time, we observe that countries that are growing and importing more than average have relatively low levels of income per capita. There is a catching-up effect of those economies investing in expanding their variety of imports.11 Figure 2 plots the average growth rate for the period 1994-2003 against the initial level of GDP per capita in 1994. There is a clear positive correlation between these two variables. If we look at productivity levels, rather than growth rates (figure 4), we observe that rich countries import a higher variety of goods than less advanced economies. The average level of imports and the average level of income per capita are positively correlated. Lower income countries have a lower extensive margin of trade. Thus, imports are a component of the technology available in the country.

3.2

Diffusion and trade

One of the drawbacks of the diffusion literature is that there are not direct measures of adoption. The evidence that I have presented so far suggests that trade can be used as an indirect measure. In this section, I use the bilateral trade data from UN COMTRADE, to present some of the characteristics of the international diffusion process in the last decade. Consistent with theoretical and empirical models of adoption (see Eaton and Kortum (1999b) and Comin and Hobijn (2004)), I find that diffusion through trade is not an instantaneous process. In table 1, I report the hazard rate of adoption over the period 1994-2003, for a sample of 37 countries that are grouped in five regions.12 The 10

The average is taken over the period 1994-2003, for a sample of thirty seven countries. The circles in red represent less developed countries in Asia, Europe, Africa, and Latin America. The circles in blue represent rich countries in Europe, Japan, and the US. 11 This catching-up effect does not apply to Africa and Latin America. These countries grow and import at negligible rates. 12 For a sample of the countries that are included in each regions, see the Appendix.

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inverse of the hazard rate represents the average time that it takes, for each importer, to adopt goods from each exporter.13 The table shows that the average diffusion lag has been between three and ten years.

3.3

Innovation and productivity

In the last decade, a common characteristic of fast growing countries is that they do not invest a significant amount of resources in doing R&D. In fact, figure 3 shows that there is a negative correlation between R&D investment and growth in trade of varieties. R&D intensity is measured as the fraction of workers that are allocated into R&D (data from the World Development Indicators in the World Bank.) Innovations are concentrated in a few rich countries, especially in Japan, the US, and Sweden. However, less innovative economies also grow, sometimes at a higher rate than their innovative counterparts. They are benefiting from innovations done elsewhere through trade. If we look at levels of productivity, we see that there is a positive correlation between the level of income per capita in the countries and the amount of resources that they invest in R&D. Consistent with the development literature, one part of the technology in a country comes from investing resources in domestic innovation. 13

I use the tools of survival analysis (or duration analysis) with censored data. I estimate a non-

parametric survival function (using the Meier Kaplan estimator with right-censored data). Ideally, we would need to know the time at which each good is invented by the exporter and the time at which is first imported by each destination. There are several limitations in the data. First, I do not observe the time of invention. I assume that this is given by the first time a source starts exporting a good to any country. There are left and right censoring in the data. There is left-censoring because, for those products that are exported in 1994, we do not know if they were invented in that year or earlier. There is right-censoring because some importers have not adopted, before 2003, all the goods that are exported. It is easy to fix the right-censoring problem, but dealing with left censored data is more problematic. It is straightforward to handle if we assume that the hazard rate does not vary with survival time. The standard way of handling left-censoring is to drop the spells that started before the window of observation.

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4

The Model

In this section, I construct an endogenous growth model of trade in varieties that captures the main features of the data. I consider a world economy composed of M countries that interact with each other through trade. Technology is embodied in new goods that are used for final production. As in Romer (1987), creation and adoption of new intermediate products are the source of embodied productivity growth.14 I also introduce a residual that represents disembodied technological progress, as in Greenwood, Hercowitz, and Krusell (1997). In each country there is a consumer that supplies labor inelastically, and consumes a non-traded final good. Each final product is produced using traded intermediate goods, which are introduced in the economy by investing resources in innovation and adoption of foreign innovations through trade. The model predicts that, in steady state, all the countries grow at the same rate and differ in relative productivity, depending on their ability to innovate and import goods. Differences in growth rates arise in the transition. Throughout the paper, whenever a variable has both a subscript and a superscript, the superscript indexes the destination of imports and the subscript indexes the source of exports. The goods are indexed by j and the time is indexed by t.

4.1

Preferences

In each country there is a representative consumer that supplies labor inelastically and, solves the maximization problem max U(Cit ) =

∞ X

β t Cit

t=0

s.t.

X

β t Cit =

X Yit (R)t

where β is the discount factor, Cit is consumption in country i at time t, R is the risk-free interest rate, and Yit is final output. 14

Other authors studying the role of trade in explaining differences in growth rates, have focused

on capital accumulation as the source of economic growth. See Ventura (1997)

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The FOC implies the relationship between the discount factor and the risk-free interest rate. β=

4.2

1 R

Final production sector

Each country i produces, at time t, a non-traded final good Yit using traded intermediate goods, j, according to the CES function Yit = eg¯ait

Tit X

1

(bintj ) σ (xinjt )

j=1

σ−1 σ

σ ! σ−1

(1)

where σ > 1 is the elasticity of substitution among differentiated intermediate goods;15 xnijt is the amount of input j that is used in the production of final output; bintj is a preference parameter that affect expenditure shares (it was introduced by Feenstra (1994) and Broda, Greenfield, and Weinstein (2008), to correct for changes in quality when a new variety is introduced); and Tit is the total number of varieties available for final production in country i at time t. It is a measure of embodied technology and it includes both domestic and foreign adopted intermediate goods. Finally, ait captures country-specific manufacturing productivity or disembodied technology, which is assumed to be common across sectors. It follows the AR(1) process ait = ρai,t−1 + uit with ρ ∈ (0, 1) and uit ∼ N(0, σ 2 ) The CES production function was first proposed by Ethier (1982). It introduces a love for variety effect by which, holding expenditures constant, an increase in intermediate goods translates into an increase in productivity. At the same time, countries with a higher level of varieties for final production, present a higher level of productivity. 15

When σ → ∞, goods are perfect substitutes.

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4.3

Intermediate production sector

In the intermediate goods sector, there is a continuum of monopolistic competitive firms, who each sell a different variety to the competitive final good producer. Intermediate goods are produced according to the same CRS production function,16 xijt = lijt with

P

j lijt

(2)

= Lit , and lijt is the amount of labor that each firm j employs to

produce in country i. Lit is the total supply of labor in the country. These assumptions have implications for pricing, firm profits and the value of having an innovation adopted in a country. Under monopolistic competition each good is produced by a separate monopolist. Markets are segmented so that producers can set a different price in each market. Producers in each country endogenously choose to produce a different set of goods.17 Taking as given the demand by the final producers, each intermediate good firm chooses a price, pint , to be a constant mark-up over the marginal cost. The value of goods that domestic final producers demand from n is xint where bint =

R

bi dj j nj

=

exp (¯ g ait )σ bint Xit



pint Pit

(−σ)

(3)

is the aggregate preference parameter, Xit = ωit Lit is total

spending by country i, ωit represents wages, and Pit is the price index

Pit =

M X

Aint pint

n=i


1−σ

1 ! 1−σ

where Aint is the number of intermediate goods from country n that have been adopted by country i at time t. Trade is assumed to be costly: there is an iceberg transport cost for the products shipped from country n to i equal to din > 1, with dii = 1. Intermediate firms’ prices 16

Labor is the only factor of production in the economy. It is assumed to be immobile across countries and perfectly mobile across sectors within a country. Labor is used for manufacturing of intermediate goods, innovation, and adoption. 17 While the Armington assumption of goods differentiated per source of exports implies that countries exogenously specialize in a different set of goods, the monopolistic competition setting implies that firms produce differentiated goods.

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differ in the domestic and the foreign market by the transport cost din .18 That is, they set a price pii,t = mω ¯ it

(4)

pni,t = m(ω ¯ it dni )

(5)

in the domestic market and

in each foreign market, with m ¯ =

σ−1 σ

as the constant mark-up.

Instantaneous profits by intermediate firms are given by the following expression i πnt

   i −(σ−1) 1 pnt ait = e ωit Li σ Pit

They depend on the expenditure on each intermediate good, which at the same time depend on the size of the country. Larger countries are a bigger source of profits.

4.4

Innovation and adoption

Within my model, the connections between trade in varieties and growth are underpinned by the mechanisms of innovation and adoption. This section explains the mechanisms by which new goods are developed in an economy and the process by which they diffuse to other countries. Both processes are endogenous and depend on profit maximization decisions by the economic agents. The microfoundations of innovation and adoption are as follows. In a given country, new goods arrive endogenously by investing resources in R&D. A competitive set of entrepreneurs bid for the right to produce the good. They need to pay the market price for an innovation, which is given by the discounted present value of profits that the entrepreneur who gets the production right will obtain by selling the good. Positive profits arise because the producers of the intermediate goods are monopolistic competitors, who set prices taking as given the demand by final producers in each potential market. There is a fixed cost to start producing the good, given by the 18

The iceberg cost effects how much of the intermediate good is shipped across countries but it

does not affect whether a new product is imported. This is determined by barriers to technology adoption, as I explain in section 4.4.2.

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investment needed to acquire the ‘design’ from the research sector. Note that in this framework, the research department is treated as a separate sector from the intermediate producers and technologies embodied in intermediate goods are transferred to the firm for a specific transfer price. Once the firm acquires the right to use the technology, it starts producing the intermediate good. This good can be sold immediately to the domestic final producers. In this sense, there is instantaneous diffusion within countries. This is not an unreasonable assumption. Eaton and Kortum (1996) estimate that the probability of diffusion within a sample of five very innovative OECD countries is very high, between 0.8 and 0.9. Diffusion to the foreign market, however, is a slow process. To sell the good abroad, the firm needs to make a costly investment to adopt the foreign product.19 Think of this as a cost of adapting the product to the specifications of the importer country. Whether the good is ready to be adopted by the destination is a random draw with a probability that depends on the amount of resources that are allocated to learn how to use the product, and a spillover effect. This is a novelty in my paper.20 The introduction of an endogenous process of adoption, instead of the purely exogenous one, implies that there are two profit maximizing decisions in this setting. On the one hand, innovators choose how much labor they want to employ in R&D by comparing the marginal cost of adding one more worker into research with the marginal benefit, which depends on the market price for an innovation. On the other hand, intermediate producers choose how much labor they want to hire in the potential destination to make their product usable there. They compare the marginal cost of adoption with the marginal benefit, which is given by the difference between the value of a good that has already been adopted and the value of a non-adopted good. The amount of labor that is allocated to one or the other activity depends on country specific parameters and the level of development. Before explaining in detail the domestic innovation and foreign adoption processes, let me introduce some notation. Zit is the stock of technologies that have been 19

The same results would hold if we think of the intermediate firm that wants to export the good as hiring the services of a third firm in the destination to adapt the products. 20 The important role of spillovers has been recently analysed by Klenow and Rodriguez-Clare (2005)

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developed in country i, and are available to be adopted at time t. Following Nelson and Phelps (1966), Zit represents the theoretical level of technology, which is the level of technology that would prevail in a country if diffusion were instantaneous. Aint is the stock of foreign technologies that country i has successfully adopted from country n. Instantaneous diffusion within the country implies that, at each moment in time, the theoretical and actual number of technologies in country i are the same, that is Aiit = Zit . Slow diffusion across countries, instead, implies that, at each moment in time, the number of adopted goods is a subset of the number of innovations, that is Aint 0 every good will eventually be available in any country. From the expression Tit = Zit +

PM

i n=1 Ant ,

the growth rate of intermediate goods

in steady state can be obtained as follows, M

∆Ti ∆Zi X ∆Ain gi = = + Ti Ti Ti n=1

(18)

Substituting equations (6) and (12) into equation (18), productivity growth in steady state can be expressed as a function of the amount of research that has been done around the world: g = gi =

αi riγr

+

M X

εin

n=1

Since Tns = Tnt (1 + g)

(t−s)

t X

γr (1 − εin )−(t−s) αns rns

s=1

Tns Tit

(19)

and rns = rn ∀s in steady state, and taking into account

that instantaneous diffusion within the country implies that εii = 1, we can rewrite equation (18) as g=

M X n=1

εin αn rnγr

−(t−s) M  X (1 − εi ) n

s=1

(1 + g)

With positive values for γr , αn , εin and rn =

=

M X n=1

Rn , Ln

εin αn rnγr

(1 + g) Tnt g + εin Tit

(20)

the Frobenious Theorem guar-

antees that we can obtain a value for the growth rate g and relative productivities Ti . Tn 31

See Benhabib and Spiegel (1994).

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It is important to note that, if there were no sources of heterogeneity in the country, that is, if αiR = αR , αiA = αA , Li = L and din = d ∀i, n, then we would reach a steady state with all the countries investing the same amount of labor into R&D and adoption, demanding the same amount of intermediate goods, and reaching the same level of income per capita.

6 6.1

Empirical strategy Bayesian Estimation

I estimate the model using Bayesian techniques.32 I use Dynare (Juillard 1996) to solve and estimate the model.33

6.2

Data and priors

To make the model more tractable, I group the sample of thirty-seven countries into five regions in such a way that countries in the same group share common characteristics (similar innovation intensity and GDP per capita growth): The United States, Japan, Western Europe, Eastern Europe and Asia.34 Keller (2004) already considered the importance of analysing the interaction between these regions when he said: ‘Many economist believe that the increased economic integration [. . . ] has tended to increase the long-run rate of economic growth. If they were asked to make a prediction, they would suggest that prospects for growth would be permanently diminished if a barrier were erected that impeded the flow of all goods, ideas and people between Asia, Europe and North America’ 6.2.1

Data

The model is fitted to annual data for the period 1994-2003, since 1993 is the first year that data at a high level of disaggregation became available for a large sample of countries. The observable variables of the model are the annual growth in imported 32

The steps of the methodology can be found in Schorfheide (1999). The code is available upon request. The variables in the code are expressed in stationarized terms, in order to be able to compute the loglinearization around the steady state. 34 The sample of countries included in each region is reported in the Appendix. 33

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varieties, data on output growth and the fraction of workers employed in R&D.35 There are one hundred and thirty-five observations corresponding to nine years, five regions of countries and three observable variables.36 Bilateral trade data are obtained from the UN COMTRADE database. I follow the HS-2000 classification, which contains goods at the 6 digit level of disaggregation, and restrict the analysis to intermediate products (the correspondent codes can be found in the appendix). Output is measured with GDP per capita PPP adjusted at constant prices of 2005 (the data come from the World Development Indicators in the World Bank). Finally, the research intensity of a country is measured by the fraction of workers that are allocated into research (data taken from the World Development Indicators in the World Bank.) I estimate the parameters behind the innovation and adoption processes, the elasticity of substitution across intermediate goods, and the shock processes. 6.2.2

Shocks

In order to have invertibility in the likelihood function, the ML approach requires as many shocks as observable variables. With three series of observable variables, we need to introduce three series of shocks. One of them is given by the neutral technology shock, ai in final production, for each region. Another is an i.i.d shock to innovation productivity, aαit . Finally, I add measurement errors to the growth rates of imported varieties, one for each region. The structural shocks and measurement errors incorporated in the estimation are ai,t = ρi ai,t−1 + uit with uit ∼ N(0, σi2 ) ξi,t ∼ N(0, σ 2 ) 35

For more details on how to compute growth in varieties, see Broda, Greenfield, and Weinstein (2008). 36 Note that there is a cross-sectional dimension in the data. DSGE models that are estimated in macroeconomics with Bayesian techniques have a long time series for one or two countries; in my case, I have a short time series sample but I add five countries in the analysis.

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gitobs = git emeit 2 with meit ∼ N(0, σme,i )

where me is the measurement error and i = 1 . . . 5. 6.2.3

Parameters

STRICT PRIORS A set of the parameters of the model is treated as fixed in the estimation (also called strict priors or calibrated parameters). The strict priors are reported in table 2; they are obtained from other studies or from steady state relations. The iceberg transport cost, din varies across pairs of countries and is proportional to distance. The productivity of the innovation process αiR , is set to satisfy equation (6). There are not available data on the number of goods that have been invented by the country. However, we can find data for the number of exported varieties. I use these data as a proxy for ∆Zit (the key assumption is that the number of exports is proportional to the number of godds produced within the country). The results show that Asia and Eastern Europe have the lowest productivity of innovation, while the US and Japan are the most productive regions.37 At the same time, note that from the optimal investment in innovation, given by equation (14), the higher the productivity αiR , the higher the fraction of workers that are allocated in R&D, everything else constant. This is consistent with the experiences of the US and Japan in the last decade: they have a higher productivity of research and a higher investment in R&D. Finally g¯ is set so that disembodied productivity represents 25% of productivity growth in steady state. Note that, in steady state, the proportion of growth that is explained by disembodied and embodied productivity is the same across countries. PRIORS The parameters to be estimated are the elasticity of substitution across intermediate goods, σ, the elasticity of adoption, γa , the extent of diminishing returns in the innovation process, γr , the cost of adoption, αiA , the persistence, ρi and the standard 37

The increase in venture capital investments in the US and policies that encourage public R&D

in Japan in the last decade, could be explaining a higher value for this parameter.

26

deviations, σi , of the neutral technology shock and productivity of innovation shocks. The priors assumed for the parameters can be found in tables 3 and 4. I assume a uniform prior for the elasticity of substitution across intermediate goods. This parameter can take any value higher than 1, which covers the whole range of possible values. The prior for the cost of adoption in each region, αiA is distributed Gamma with mean 1.2 and standard deviation 0.25. The mean is set to match the hazard rates in table 1, which determine the rate of adoption. The prior for the diminishing returns in the innovation process, γr , is set to a uniform (0,1). There are discrepancies on the value of this parameter. Eaton and Kortum (1999a) find a value for this parameter around 0.2. Different from this result, Griliches (1990) estimates this parameter using the number of new patents as a proxy for technological change, and obtains estimates between 0.5 and 1. The elasticity of adoption with respect to effort γa , is assumed to follow a Beta distribution with mean 0.5 and standard deviation 0.15. This parameter has been calibrated by Comin and Gertler (2006) and Comin, Gertler, and Santacreu (2008), who find that a reasonable value in a closed economy model is 0.8. Since there are not any good measures of adoption expenditures or adoption rates, they use as a partial measure the development costs incurred by manufacturing firms to make the goods usable (this is a subset of R&D expenditures). Then, they regress the rate of decline of the relative price of capital with respect to the partial measure of adoption costs. The idea is that the price of capital moves countercyclically with the number of new adopted technologies, and therefore is the measure of embodied adoption. The regression yields a constant of 0.8. Finally, in the shock processes, I assume a Beta distribution with mean 0.5 and standard deviation 0.25 for the persistence parameter, and an Inverse Gamma distribution is assumed for the standard deviation of the shocks. This guarantees a positive variance.

6.3

Estimation results

Tables 3 and 4 report the results from the estimation. The table contains the prior and posterior mean of the estimated parameters as well as 95% confidence intervals. The posterior mean for the elasticity of substitution across intermediate goods is

27

4.2. Broda, Greenfield, and Weinstein (2008) estimate that the median elasticity of substitution for a sample of 73 countries is 3.4. The value that I obtain lies between the value obtained in microeconomic models and the value obtained in macroeconomic models. The posterior mean for the adoption costs, reported in table 4, lies between 1 and 1.4 for the blocs considered in the analysis. It does not follow a particular pattern. These results can be used to compute the probability of adoption predicted by the model, εint . The average probability of adoption for the period 1994-2003 is presented in the last column of table 5. The results imply that the average time that it takes for a country to be able to use an intermediate good developed elsewhere, which corresponds to the inverse of the probability of adoption, lies between two and ten years. The posterior mean for the elasticity of innovation γr , is 0.24, similar to the results in Eaton and Kortum (1999a), and lower than in Griliches (1990). The elasticity of adoption is estimated to be 0.2, lower than what Comin and Gertler (2006) find.

28

6.4

How well does the model fit the data?

This section checks how well the model fits the data. by comparing several variables of the model for which we can find a counterpart in the data. I compare the rate of adoption and the relevant correlations between trade, innovation and productivity, shown in section 3. RATE OF ADOPTION First, I compare the actual value for the hazard rate or probability of adoption, computed with Survival Analysis techniques, as explained in section 3 to the estimated probability of adoption predicted by the model. The results are reported in table 5. The model does a good job in capturing the average adoption probability for the five regions considered in the analysis. We can also see the performance of the model in capturing the rate of adoption in figure 5. The figure reports the actual data and the rates predicted by the model. The two values are very close for most pairs of regions. UNCONDITIONAL MOMENTS In this section, I compute the correlations between trade, productivity and innovation that are predicted by the model. Using the posterior mean of the estimated parameters and the standard deviations of the shocks, I simulate the model, and obtain the correlations of the simulated variables representing R&D, output growth, and growth in imported varieties. The results are presented in table 6. Overall, the model does fairly well in reproducing the relevant moments.

6.5

Identification

In this section, I explain how the estimated parameters are identified from the data on R&D, productivity and trade. I take advantage of the panel dimension of the data to compute unconditional moments across time and across countries, for different values of the parameters. What I observe is that different parameters affect different moments in the data, as I explain below. The parameter in the final production function, σ, represents both, the love-forvariety effect, and the elasticity of demand for intermediate products. In the first case, it captures the extent by which an increase in intermediate goods that are used for final production, translates in an increase of output. Since R&D, 29

both domestic and foreign, is embodied in the intermediate goods, σ establishes a relationship between research intensity and embodied productivity growth. A lower σ implies a stronger correlation. First, for a given investment in domestic R&D, a lower elasticity of substitution implies a higher growth rate of income per capita (‘love for variety effect’). The effect is not linear, and it depends on the level of development of the country: growth in embodied productivity in a destination country is a weighted average of domestic and foreign R&D (see equation (20)). The weights are given by the ratio of the relative income per capita in each source country with respect to the destination, which is higher in developing countries. Therefore the impact of foreign R&D in developing countries is higher than in developed economies. For the same investment in R&D, output growth increases everywhere but it does so proportionally more in developing countries (see figure 6a vertical arrows). Second, for a given output growth, a decrease in σ affects the demand for intermediate goods in a different way, depending on the origin of the good and the level of development of the country . Note that, from equation (3), the elasticity of demand for intermediate goods with respect to changes in σ is negative. In the case of foreign goods the elasticity is lower for developing than for developed countries. That is, when there is a decrease in the elasticity of substitution, the demand for foreign goods in developing countries increases less than the demand for domestic products. Therefore, developing countries allocate more resources into innovation. The opposite is true in developed countries. They demand more foreign products and allocate less resources into innovation (see horizontal arrows in figure 6a). The parameter γr describes the elasticity of innovation with respect to research intensity. It affects the correlation between growth in imported varieties and research intensity across countries, which becomes more negative, the higher is γr . On the one hand, an increase in γr increases investment in domestic R&D through the optimality condition in equation (14), everything else constant. The increase in R&D is higher in developed than in developing economies. The reason is that the relative cost of innovation with respect to adoption decreases with the level of development. Therefore, and increase in γr increases R&D proportionately more in developed economies (horizontal line in figure 6b). On the other hand, γr represents the elasticity of new domestic intermediate goods 30

with respect to research. For a constant research intensity, an increase in γr increases the number of domestically produced goods, through equation (6). This increase in higher in developed countries, because the spillover effect is stronger (remember that rich countries have a higher extensive margin of trade). The gap increases and through the catching-up effect growth in imports in developing countries will increase, despite of the higher investment in domestic research. The opposite is true for developed countries (see vertical axis in figure 6b). Finally, the parameter γa affects the correlation between trade in imported varieties and economic growth. Note that if γa were zero, the positive correlation between imports and growth would be entirely driven by the catching-up effect; therefore, we would expect countries in Africa and Latin America to follow the same patterns as Asia and Eastern Europe, because investment in adoption would be irrelevant. Instead, if γa is strictly positive, the correlation between trade and growth depends on both, the catching-up effect and the trade-off between allocating resources to domestic or foreign innovations. Changes in the elasticity of adoption induce changes in the correlation between trade and growth. First, if γa increases, countries allocate more resources into doing adoption (optimality condition in equation (15). Therefore, growth in imports increases, proportionally more in developing countries (see horizontal arrow in figure 6c). Second, if we keep investment in adoption constant, an increase in γa also increases output growth, and once again, proportionally more in developing countries, that benefit from the catching-up effect (see vertical arrow in figure 6c). The correlation becomes stronger, as we place more weight on investment in adoption. The results suggest that catching-up is not driving all the results in the model. In this framework, endogenous technology diffusion is a key element to understand the connections between trade and growth. So far, I have focused on the identification of the parameters that are common across countries. I identify these parameters from the cross-section dimension of the panel of data. The country-specific parameters, αia are identified from the time series dimension of the data. αiA and αiR are not separately identified. We do not have data on Zi . αiA is identified from correlation across time between R&D and trade. The higher is the parameter for each country, the more negative will be the correlation between innovation and trade; countries will allocate more resources into adoption 31

and less into innovation.

7

Contribution of domestic and foreign sources of innovation to growth

This section analyses the sources of productivity growth in each region, in order to assess the quantitative importance of foreign R&D though imports. Using the posterior mean of the estimated parameters, I decompose the growth rate in the total number of technologies into the contribution of domestic and foreign sources of innovation. Equation (6) can be used to evaluate the domestic contribution to embodied growth. The relevant parameters are the productivity parameter, αiR and the scale effect, γr . The contribution of foreign sources of innovation is given by expressions (8) and (7). The relevant parameters are the adoption costs, αiA and the elasticity of adoption. γa . The decomposition is presented in table 7. Each row represents the destination (importer), while each column represents the source (exporter). Thus, an entry in the matrix reports the percentage in the growth rate of embodied productivity in each destination that is explained from technologies developed in each source, averaged over the period 1994-2003. The diagonal, in bold numbers, measures the contribution of domestic sources innovation. The results show that nearly 83% of the productivity growth in Asia can be explained by foreign innovations embodied in imports, especially from the US and Japan. The US has by far the highest percentage of growth accounted for by domestic innovation, with 47% of its embodied productivity coming from its own innovative effort. Japan, with 32 %, and Western Europe, with 43% follow the US. The results are consistent with the empirical evidence: Asia does relatively little research, but has experienced a rapid increase in imported varieties, especially from the US and Japan, which are the most innovative regions. Around two thirds of the contribution of foreign sources of innovation in Europe and Asia proceed from Japan and the US. Asia and Eastern Europe’s innovations only contribute around 10% and 20% to embodied productivity growth in the other 32

regions. Table 8 reports the contribution of each column-exporter’s innovations to each row-importer’s technological progress. The US and Japan are the main sources of innovations, while Asia is the country that contributes the least to technological progress in the other regions. Note that to obtain the decomposition in tables 7 and 8, I have not used data on exported varieties, but data on research intensity as the measure of innovation. What I do next is to compute the same decomposition, using bilateral exports from each source to each destination. Table 9 reports the percentage of each row-importer’s total imports that is explained by each column-exporter. The results are very similar to the ones where only innovation data are used. In Asia, 4.08% of total imports in varieties comes from less innovative countries in Europe. The US and Japan together represent more than 50% of imported varieties in each region. Asia and less innovative EU contribute the least. There is a distance effect, however, that is not present in table 8. More innovative Europe represents a higher percentage than Japan in the imports of less innovative Europe. Asia and more innovative Europe contribute almost the same to Japan’s imports, even though Asia only represents 7% of the research intensity in the five regions world. Furthermore, more than 60% of the innovation effort is done in the US and Japan. It is not surprising then that these countries are benefiting, mainly, from domestic sources of innovation. The results suggest that the assumption that R&D is embodied in exports seems a reasonable one. The discrepancies between the two tables could reflect factors embodied in exports rather than R&D.

8

Speed of convergence: Where will the world be in the long run?

In this section, I compute for each country the speed of convergence to the technology frontier that is, to the levels of income per capita of the US, considered the baseline economy. To do that, I take the estimated value of the structural parameters and the standard deviation of the shocks, and simulate the model for 1000 periods. The results are reported in table 10. Japan and Western Europe start from a 33

relatively closer position to the technology frontier, while Asia and Eastern Europe lag behind. The second column in table 10 shows that at one extreme, Asia’s income per capita in 1995 was 25% of the income per capita in the US. At the other extreme lies Japan, with 80% of the US income. Europe lies in the middle: Eastern Europe is closer to Asia and Western Europe is closer to Japan. The first and third columns in table 10 show how close each region will get to the technology frontier once they reach the steady state. Asia will improve its position by 200%. That means that, in the new steady state, Asia’s income per capita will be 80% that of the US. Japan, which is closer to the US, only improves by 20% and its income per capita in steady state will be 96% of the US. Countries that lag behind (Asia and Eastern Europe) take longer to get closer, but their improvement is higher. The gap is reduced at a lower rate the closer countries get to the steady state, as convergence predicts. The table also shows that Asia will get to the half life steady state in 80 years. Japan will do it in 30 years. Note that the technology frontier is moving forward due to investment in innovation in every country. In steady state, countries close the gap, but there is not complete catching up in levels of income per capita. This can be explained by differences in policies and institutions, which are reflected in country specific parameters of innovation, and adoption.38

38

This fact was already observed by Klenow and Rodriguez-Clare (2005).

34

9

Counterfactuals

In this section, I perform two experiments to show how shocks to innovation and adoption can explain the connections between trade and growth that we observe in the data. Suppose that we start from the steady state of the model and we introduce two policy changes: • First, a 50% permanent decrease in the barriers to technology transfer in Asia, that is, an increase in αA (Asia) in equation (7). • Second, a 50% permanent increase in the productivity of innovation in Asia, that is, an increase in αR (Asia) in equation (6). I explore the transition to the new equilibrium, and perform comparative statics between the two steady states. Under the assumption that the US represents the technology frontier, I analyse the effect that the two shocks have for world growth rates, research intensity, adoption, country growth, the extensive margin, and the relative income per capita in Asia and the US. The two experiments lead simultaneously to higher trade and faster growth.

9.1 9.1.1

Counterfactual: Reduction in adoption costs in Asia Steady State

A 50% reduction in the cost of adoption in Asia increases world growth rates by 0.7%. Table 11 presents the comparative statics for the key variables in the analysis. Faster adoption results in a higher research intensity in the new steady state of every country. In Asia, this increase is driven by the ‘spillover effect’ in equation (6). Research intensity in this region is 2.3% higher than in the initial steady state. The result is a higher diversification of exports of the region, driven by a decrease in the costs of adoption. The higher ability to adopt goods increases the demand for imports, especially from Japan and the US. Recall from previous sections that these two regions are the main exporters in the sample. This ‘demand effect’ increases the present discounted value of future profits from selling a good abroad, which increases the market price for an innovation and, therefore research intensity in the trading partners of Asia. 35

The rate of adoption in Asia increases for two reasons: directly, from a decrease in the costs of adoption, that is, an increase in αA (Asia); indirectly, first, from an i increase in the investment in adoption, Hnt and, second, from an increase in the

proportion of new goods that Asia imports from the US,

Aint Znt

.

Higher adoption has positive implications for the extensive margin in Asia, relative to the US. Asia closes the distance with respect to the technology frontier, both in the number of varieties that it produces domestically, and in proportion of goods that it adopts from the technology frontier. This catching-up is reflected in an increase in relative wages of Asia with respect to the US by 70%. Despite getting closer, there is still a gap in levels of income per capita between both countries. At the new steady state, growth rates are constant and common across countries. There is convergence in growth rates but not of levels. 9.1.2

Transitional Dynamics

Figure 7 represents the transition path for the main variables after a 50% permanent reduction in the barriers of adoption in Asia. In the first panel of figure 7, we see that the research intensity in Asia (solid line) decreases upon impact. There is an initial reallocation of resources into adoption and away from research. Asia starts importing more varieties, and after one period, the increase in imported varieties reduces the cost of innovation, through the spillover effect. Research intensity increases then, and it reaches a higher level in the new steady state. A higher value of αA (Asia) implies that the value to adopt new technologies , and therefore investment in adoption increase. This occurs at the intensive and extensive margins (solid and dashed line in the first panel): Asia imports more goods and more of the same goods. The ‘demand effect’ increases research intensity in the US, which reaches a higher level in steady state (dashed line in the first panel). Eventually, Asia becomes closer to the US, through an increase in both imported and domestic varieties. Asia has been growing faster than the US. However, although the gap is smaller, wages, a proxy for income per capita, are still higher in the US (fourth panel). This experiment generates both higher trade and faster growth, but the initial causation goes from more trade to more growth. 36

Note that this scenario reproduces the situation that we observe in the data. In the transition, rich countries are allocating more resources into R&D, while less advanced countries in Asia are adopting new goods. This translates into faster growth. However, Asia still lies behind the US in levels of income per capita, due to the initial differences caused by country-specific parameters reflecting innovation productivity. Thus, adoption alone is not sufficient to completely close the gap.

9.2

Counterfactual: Increase in productivity of innovation in Asia

9.2.1

Steady State

A 50% increase in the productivity of innovation in Asia increases world growth rates by 3%. Table 12 presents the comparative statics for the key variables in the analysis. Research intensity in the new steady state is higher for Asia, but lower for its trading partners. First, a higher productivity of innovation, reduces the cost for this activity in Asia upon impact. Second, after the first periods, the ‘spillover effect kicks in. All this results in an increase in the research intensity of the region by 90%. The initial drop in research intensity in the US is driven by a negative ‘demand effect’ from Asia. After some periods research intensity in the US increases. As in the previous experiment, Asia closes the distance with respect to the technology frontier, both in the number of varieties that it produces domestically, and in the proportion of goods that it adopts from the technology frontier. Relative wage with respect to the US increases by 40%. In this experiment, Asia does not completely closes the gap with respect to the US. In fact, the increase in relative wages is lower than in the previous experiments. As the country is further away from the technology frontier, adoption policies are more effective than innovation policies. 9.2.2

Transtional Dynamics

Figure 8 represents the transition path of the positive productivity shock in Asia. In the transition, the research intensity in this region goes up (solid line in the second panel). A higher αR (Asia) decreases the cost of innovation, which implies a reallocation of labor into research. In the US, there is, upon impact, a reduction in research

37

intensity. The initial drop is driven by an initial reallocation in Asia from adoption into research, which initially decreases the demand by this region. After some periods, it starts increasing, mainly because Asia starts demanding products from this country (first panel in figure 8). In the transition, Asia is closing the gap with respect to the leader through an increase in imported varieties (first panel) and an increase in innovations (first panel). Relative wages of the US decrease, but less than in the previous experiment. Adoption policies seem adequate when the country is far away from the technology frontier, since in that case the costs of innovation are higher than the costs of adoption. As the country becomes more developed, the costs of innovation go down. However, without active policies that incentive research, there will not be complete catching up in levels of income per capita. Once the country has built a certain level of technology, policies that incentive innovation become important to keep growing.

38

10

Conclusions

The effects of trade on growth have been studied extensively in economics. However, there are still two gaps in these studies. First, the mechanisms by which countries benefit from each other’s technologies through trade are not fully understood. Second, the magnitudes are unknown. This paper show that innovation, through creation of new varieties, and diffusion, through adoption of foreign goods through imports, provide the mechanisms to explain the connections between trade and growth. In my paper, trade in varieties arises as the new way to measure the extent of trade, and therefore diffusion, in an open economy. This paper is one step forward in analysing the connections between trade in varieties and growth. It constitutes a theoretical contribution to the empirical literature in the area. First, it does not face the endogeneity problem of regression analysis. Second, the model is tractable enough to analyse the mechanisms outside of steady state. This is important to capture differences in growth rates across countries. Third, Bayesian techniques allow me to incorporate prior knowledge into the analysis and pin down the value of the parameters that govern innovation and adoption. I find that diffusion in the last decade has been particularly important in Asia and Eastern Europe, allowing these countries to benefit from their backward situation and grow faster than average. Innovation, instead, is more important in the US, Japan, and Western Europe. The model suggests that, as countries become technologically more advanced, they should focus on policies that increase innovation. For countries that lag behind, their best option is to adopt foreign technologies, through imports. As countries get closer to the technological frontier, a policy that fosters innovation is more adequate.

39

References Acemoglu, D., P. Aghion, and F. Zilibotti (2002): “Distance to frontier, selection, and economic growth,” NBER Working Paper 9066. Benhabib, J., and M. Spiegel (1994): “The role of Human Capital in Economic Development: Evidence from aggregate cross-country data,” Journal of Monetary Economics. Broda, C., J. Greenfield, and D. E. Weinstein (2008): “From Groundnuts to Globalization: A Structural Estimate of Trade and Growth,” NBER Working Paper 12512. Broda, C., and D. E. Weinstein (2006): “Globalization and the Gains from Variety,” Quarterly Journal of Economics. Cameron, G., J. Proudman, and S. Redding (2005): “Technological Convergence, R&D, trade and productivity growth,” European Economic Review. Coe, D. T., E. Helpman, and A. W. Hoffmaister (1997): “North-South R&D spillovers,” The Economic Journal, 107. Comin, D., and M. Gertler (2006): “Medium Term Business Cycles,” American Economic Review. Comin, D., M. Gertler, and A. M. Santacreu (2008): “Future Technology, Endogenous Diffusion, Economic Fluctuations and the Stock Market,” Working Paper. Comin, D., and B. Hobijn (2004): “Cross-country technology adoption: making the theory face the facts,” Journal of Monetary Economics. Cummins, J. G., and G. L. Violante (2002): “Investment-Specific Technical Change in the US (1947-2000): Measurement and Macroeconomic Consequences,” Review of Economic Dynamics. Easterly, W., and R. Levine (2001): “It’s not factor accumulation: Stylized Facts and Growth Models,” World Bank Economic Review. 40

Eaton, J., and S. Kortum (1996): “Trade in ideas: Productivity and patenting in the OECD,” Journal of International Economics. (1999a): “International technology diffusion: Theory and measurement,” International Economic Review. (1999b): “International technology diffusion: Theory and measurement,” International Economic Review. (2001): “Trade in capital goods,” European Economic Review. (2002): “Technology, Geography and Trade,” Econometrica. (2007): “Technology in the Global Economy: A Framework for Quantitative Analysis,” Unpublished Manuscript. Ethier, W. J. (1982): “National and international returns to scale in the modern theory of international trade,” The American Economic Review. Feenstra, R. (1994): “New Product Varieties and the Measurement of International Prices,” American Economic Review. Greenwood, J., Z. Hercowitz, and P. Krusell (1997): “Long-run implications of Investment-Specific Technological Change,” The American Economic Review. Griliches, Z. (1957): “Hybrid Corn: An Exploration in the Economics of Technological Change,” Econometrica. (1990): “Patent Statistics as Economic Indicators: A Survey,” Journal of Economic Literature. Hallward-Driemeier, M. (2000): “Exports and manufacturing productivity in East asia: A Comparative Analysis with Firm-Level Data,” NBER Working Paper 8894. Howitt, P. (2000): “Endogenous Growth and Cross-Country Income Differences,” American economic Review.

41

Hummels, D., and P. Klenow (2002): “The variety and quality of a Nation’s trade,” NBER Working papers 8712. Jovanovic, B. (Forthcoming): “The Technology Cycle and Inequality,” Review of Economic Studies. Juillard, M. (1996): “Dynare: a program for the resolution and simulation of dynamic models with forward variables through the use of a relaxation algorithm,” CEPREMAP working papers 9602. Keller, W. (1998): “Trade and Transmission of Technology,” mimeo, University of Texas at Austin. Keller, W. (2004): “International Technology Diffusion,” Journal of Economic Literature. Klenow, P., and A. Rodriguez-Clare (2005): “Externalities and Growth,” Handbook of Economic Growth. Krugman, P. (1979): “A model of innovation, technology transfer and the world distribution of income,” Journal of Political Economy. Nelson, R., and E. Phelps (1966): “Investment in humans, technological diffusion, and economic growth,” American Economic Review. Parente, S. L., and E. C. Prescott (1994): “Barriers to technology adoption and development,” The Journal of Political Economy. Phelps, E. (1964): “Models of Technical Progress and the Golden Rule of Research,” Cowles Foundation Discussion Papers 176, Cowles Foundation, Yale University. Rivera-Batiz, L., and P. Romer (1991): “International trade with endogenous technological chenge,” European Economiv Review. Romer, P. (1987): “New Theories of Economic Growth: Growth based on increasing returns due to specialization,” AEA papers and proceedings. Santacreu, A. M. (2006): “Differences in growth rates: The role of innovation and technology diffusion,” NYU mimeo. 42

Schorfheide, F. (1999): “Loss Function Estimation of Forecasting Models: A Bayesian Perspective,” American Statistical Association, Proceedings of the Section on Bayesian Statistics. Teece, D. (1977): “Technological Transfer by Multinational Firms: The Resource Cost of Transferring Technological Know-How,” Economic Journal. Ventura, J. (1997): “Growth and Interdependence,” Quarterly Journal of Economics. Young, A. (1991): “Learning by doing and the dynamic effects of international trade,” The Quarterly Journal of Economics.

43

Tables and graphs 1.5

11

Growth in imported varieties .5 1

LVA LTU

ISL TUR SAU BRA

0

CHE ITA ARG JPN DEU

0

SVK

IND HRV

CHN

IRL

THA CZE SVN ESP KOR IDN FIN DNK AUT NOR GRC FRAUSA HUN PRT CYP GBR SWE SGP BEL MLT HKG BEL NLD

2

4 GDPpc growth

Developed Countries

6

8

Developing Countries

Figure 1: Relation between GDPpc growth and variety growth

8

CHN LVAEST MAC

LTU

GDPpc Growth 4 6

VNM IRL IND HRV LKA ROM BGR TUR

SVK HUN

KOR SVN CZE

THA

2

PHL IDN

DZA

ARG BRA

MLT PRT

SGP

FIN GRC ESP CYP

ISL SWE GBR

HKG

NLD AUT BELDNK FRA DEU ITA JPN

NOR USA CHE

0

SAU

0

10000

20000 GDPpc PPP (t=1995)

Developed Countries

30000

40000

Developing Countries

Figure 2: Relation between GDPpc growth and initial level of GDPpc: PPP adjusted; Average over 1994-2003es

44

1.5 Growth in imported varieties .5 1

LVA LTU

IND CHN

HRV

SVK

ISL

TUR IRL

CZE

THA IDN BRA

ESPSVN KOR DNK AUT NOR FRA USA GBR CHE SWE SGP JPN BEL BEL DEU NLD

FIN

0

GRC HUNPRT CYP ITA ARG MLT HKG

0

2000

4000 R&D Labor

Developed Countries

6000

8000

Developing Countries

Figure 3: Relation between R&D investment and variety growth: PPP adjusted;

Level of GDPpc PPP (2005) 10000 20000 30000 40000

Average over 1994-2003

NOR USA

SGP DNK JPN

IRLHKG

ISL

FIN GRC

CHE NLD AUT BEL SWE BEL

FRAGBR ITA

DEU

ESP

CYP SAU SVN PRT KOR

MLT

LVA

LTU ARG

CZE

HUN SVK HRV TUR BRA THA IDN IND

0

CHN

20000

40000

60000 Level of imported varieties

Developed Countries

80000

100000

Developing Countries

Figure 4: Relation between GDPpc and number of imported variety: PPP adjusted; Average over 1994-2003

45

Exporter

Importer

Hazard

EU+

Asia

0.31

EU-

Asia

0.19

Japan

Asia

0.35

US

Asia

0.34

Asia

EU+

0.28

EU-

EU+

0.33

Japan

EU+

0.29

US

EU+

0.28

Asia

EU-

0.24

EU+

EU-

0.33

Japan

EU-

0.31

US

EU-

0.34

Asia

Japan

0.35

EU+

Japan

0.28

EU-

Japan

0.20

US

Japan

0.25

Asia

US

0.35

EU+

US

0.29

EU-

US

0.32

Japan

US

0.28

Table 1: Hazard rates EU+ (Western Europe); EU- (Eastern europe); Japan (includes Korea)

46

parameter

value

Description

β

0.97

Discount factor

d(Asia, EU−)

1.30

Iceberg transport costs

d(Asia, EU+)

1.30

Iceberg transport costs

d(Asia, Japan)

1.10

Iceberg transport costs

d(Asia, US)

1.30

Iceberg transport costs

d(EU−, EU+)

1.05

Iceberg transport costs

d(EU−, Japan)

1.40

Iceberg transport costs

d(EU−, US)

1.30

Iceberg transport costs

d(EU+, Japan)

1.40

Iceberg transport costs

d(EU+, US)

1.30

Iceberg transport costs

d(Japan, US)

1.30

Iceberg transport costs

g¯

0.02

Disembodied growth in steady state

0.0082

Innovation productivity

α (EU−)

0.0186

Innovation productivity

αR (EU+)

0.0237

Innovation productivity

α (Japan)

0.0288

Innovation productivity

αR (US)

0.0268

Innovation productivity

αR (Asia) R

R

Table 2: Calibrated parameters

47

Parameter

Prior

Mean

5%

95%

σ

Uniform(1, ∞)

4.20

4.16

4.23

Gamma(1.2, 0.25)

1.30

1.22

1.37

α (EU−)

Gamma(1.2, 0.25)

1.18

1.02

1.35

αA (EU+)

Gamma(1.2, 0.25)

1.13

1.01

1.29

α (Japan)

Gamma(1.2, 0.25)

1.29

1.18

1.40

αA (USA)

Gamma(1.2, 0.25)

1.21

1.14

1.27

γa

Normal(0.5, 0.15)

0.19

0.14

0.22

γr

Uniform(0, 1)

0.24

0.24

0.24

αA (Asia) A

A

Table 3: Prior and posterior for the structural parameters For the Beta distribution, the number in parenthesis correspond to the mean and standard deviation

48

Parameter

Prior

Mean

5%

95%

σ(Asia)

IGamma(0.25,∞)

0.19

0.12

0.28

σ(EU−)

IGamma(0.25,∞)

0.20

0.14

0.27

σ(EU+)

IGamma(0.25,∞)

0.04

0.04

0.05

σ(Japan)

IGamma(0.25,∞)

0.04

0.04

0.04

σ(US)

IGamma(0.25,∞)

0.09

0.06

0.10

σ r (Asia)

IGamma(0.25,∞)

0.83

0.66

0.96

σ (EU−)

IGamma(0.25,∞)

0.58

0.55

0.62

σ r (EU+)

IGamma(0.25,∞)

0.29

0.28

0.29

σ (Japan)

IGamma(0.25,∞)

0.52

0.44

0.61

σ r (US)

IGamma(0.25,∞)

0.31

0.30

0.32

me(Asia)

IGamma(0.50,∞)

2.13

2.07

2.20

me(EU−)

IGamma(0.50,∞)

2.54

2.37

2.71

me(EU+)

IGamma(0.50,∞)

0.81

0.7811

0.84

me(Japan)

IGamma(0.50,∞)

1.77

1.64

1.91

me(US)

IGamma(0.50,∞)

0.62

0.59

0.65

r

r

Table 4: Prior and posterior for the shock processes

49

Exporter

Importer

Hazard

Estimated average

EU+

Asia

0.31

0.22

EU-

Asia

0.19

0.24

Japan

Asia

0.35

0.21

US

Asia

0.34

0.19

Asia

EU+

0.28

0.27

EU-

EU+

0.33

0.26

Japan

EU+

0.29

0.23

US

EU+

0.28

0.20

Asia

EU-

0.24

0.20

EU

EU-

0.33

0.18

Japan

EU-

0.31

0.26

US

EU-

0.34

0.24

Asia

Japan

0.35

0.26

EU+

Japan

0.28

0.23

EU-

Japan

0.20

0.25

US

Japan

0.25

0.21

Asia

US

0.35

0.29

EU+

US

0.29

0.26

EU-

US

0.32

0.28

Japan

US

0.28

0.25

Table 5: Hazard rates and estimated steady state values: MSE=0.01

50

Speed of Diffusion .15.2.25.3.35 0

5

10 Pair of Regions data

15

20

predicted

Figure 5: Rate of Adoption

Correlation

Model

Data

(R&D, Trade)

-0.21

-0.32

(Growth, Trade)

0.70

0.60

(Growth, R&D)

-0.31

-0.28

Table 6: Comparison of unconditional moments: model versus data

51

To—From

Asia

EU-

EU+

Japan

US

Asia

16.98

9.78

26.95

17.54

28.75

EU-

11.90

14.64

23.36

20.50

29.60

EU+

10.09

5.62

41.94

17.35

25.00

Japan

9.29

8.87

24.56

31.99

25.29

US

9.17

7.35

21.19

15.02

47.27

Table 7: Sources of growth predicted by the model: domestic and foreign innovation (percentage; Columns (exporter); rows (importer))

To—From

Asia

Asia

EU-

EU+

Japan

US

11.8

32.5

21.1

34.6

27.4

24.0

34.7

29.9

43.0

EU-

13.9

EU+

17.4

9.7

Japan

13.7

13.0

36.1

US

17.4

13.9

40.2

37.2 28.5

Table 8: Foreign Sources of Growth: bilateral contribution predicted by the model (percentage; Columns (exporter); rows (importer))

52

To—From

Asia

Asia

EU-

EU+

Japan

US

4.1

19.2

36.3

40.4

37.1

15.9

37.6

22.9

47.4

EU-

9.3

EU+

14.3

15.5

Japan

20.0

5.4

22.6

US

20.9

10.9

31.1

51.9 37.1

Table 9: Foreign Sources of Growth: bilateral contribution in the data (percentage; Columns (exporter); rows (importer))

Region

Years to convergence

Relative income pc (1995) Improvement

Asia

80

25%

70%

Eastern europe

70

26%

66%

Western Europe

35

69%

30%

Japan

30

80%

20%

Baseline

Baseline

US

Table 10: Speed of Convergence

53

Baseline

10 9 8

Output growth

7 6 5 4 3 2 Love for variety 1 Elasticity of demand 0

0

2

4 6 R&D intensity

8

10

8

10

(a) Identification σ 10 9 8

Growth in imports

7 6 5 4 3 2

Optimal R&D

1 Catching−up effect 0

0

2

4 6 R&D intensity

(b) Identification βr 10 9 8

Output growth

7 6 Catching−up effect 5 Optimal adoption

4 3 2 1 0

0

2

4 6 Growth in imports

54 (c) Identification βa

Figure 6: Identification

8

10

Z

/Z

Asia

US

(solid); AAsia/Z US

(Dashed)

US

0.3

0.9

0.28

0.85

−4 −3 Research Intensity (solid Asia; Dashed US) x 10 x 10

5.5

3.05

5

3

4.5 0.26

0

10

20

0.8 40

30

4

0

10

20

2.9 40

30

Relative wages wAsia/wUS

Growth Rates (solid Asia; Dashed US) 0.045

2.95

0.9 0.8

0.04

0.7 0.035 0.03

0.6 0

10

20

30

40

0.5

20

40

Figure 7: Permanent reduction in barriers to adoption in Asia

55

60

80

100

120

140

Variable

% change

∆r(Asia)

2.3%

∆r(US)

2.6%

∆g

∗

0.7%

∆ ω(Asia) ω(U S) ∆ Z(Asia) Z(U S) AAsia ∆ ZUUSS

70% 11% 10%

Table 11: Reduction in adoption barriers in Asia: Steady State Comparison

56

Z

/Z

Asia

US

(solid); AAsia/Z US

(Dashed)

US

0.45

0.84

0.4

0.83

0.35

0.82

0.3

0.81

0.25

0

10

20

0.8 40

30

−4 −3 Research Intensity (solid Asia; Dashed US) x 10 x 10

10

8

2.95

6

2.9

4

0

10

20

2.85 40

30

Relative wages wAsia/wUS

Growth Rates (solid Asia; Dashed US) 0.033

3

0.7 0.65

0.032

0.6 0.031 0.03

0.55 0

10

20

30

40

0.5

20

40

60

Figure 8: Permanent increase in innovation productivity in Asia

57

80

100

120

140

Variable

% change

∆r(Asia)

88%

∆r(US)

-3%

g

∗

3.2%

ω(Asia) ω(U S) ∆ Z(Asia) Z(U S) AAsia ∆ ZUUSS

40% 37% 2%

Table 12: Increase in innovation productivity in Asia: Steady State Comparison

58

12

Appendix A

Country

GDPpcgrowth

Varietygrowth

Researchers

GDPpc(1995)

Austria

1.94

0.03

2.72

28401.87

Belgium

1.93

0.16

2.89

26668.76

Bulgaria

2.17

0.83

0.56

6924.32

China

8.13

0.55

0.42

1853.45

Cyprus

2.39

0.71

4.05

20212.69

Denmark

2.03

0.30

2.21

28323.68

Estonia

6.16

0.85

6.65

7911.48

Finland

3.38

0.40

2.95

21865.56

France

1.75

0.03

3.10

25856.33

Germany

1.38

0.04

1.26

26970.08

Greece

2.88

0.24

1.32

20861.02

HK

1.79

0.59

1.32

27175.87

Hungary

3.87

0.26

0.10

11048.27

India

4.20

1.96

0.21

1403.71

Indonesia

1.78

1.93

2.28

2815.82

Ireland

6.54

0.34

2.28

21328.97

Italy

1.52

0.01

1.19

25151.35

Japan

0.72

0.13

5.17

27551.29

Korea

4.37

0.28

2.70

14716.83

Latvia

6.04

1.22

1.33

6190.58

Lithuania

4.28

1.20

2.17

7402.13

Malaysia

2.81

1.11

0.28

9296.93

Malta

2.69

1.46

0.70

16839.78

Netherlands

2.21

0.47

2.53

28186.20

Philippines

1.78

1.19

0.05

2415.27

Poland

4.53

0.41

1.48

8836.75

Portugal

2.26

0.20

1.65

16543.51

Romania

2.45

0.69

1.06

7223.41

Singapore

3.08

0.43

3.89

30922.08

Slovakia

3.99

0.54

1.86

10651.25

59

Country

GDPpcgrowth

Varietygrowth

Researchers

GDPpc (1995)

Slovenia

3.74

0.15

2.32

15410.37

Spain

2.75

0.08

1.78

20887.66

Sweden

2.56

0.15

4.85

24843.19

Thailand

2.39

0.50

0.22

5907.27

UK

2.72

0.05

2.99

24555.60

USA

2.04

0.07

4.50

33759.57

Vietnam

5.78

1.79

0.16

1214.14

Asia

3.53

1.12

0.98

9222.73

EU less R&D

3.64

0.57

1.91

13963.97

EU more R&D

2.21

0.18

2.83

26185.70

Japan

2.55

0.20

3.94

21134.06

USA

2.04

0.07

4.50

33759.57

60

13

Appendix B Bloc

Country Code

Country Name

Africa

SAU

Saudi Arabia

Asia

CHN

China

Asia

HKG

China, Hong Kong SAR

Asia

IDN

Indonesia

Asia

IND

India

Asia

SGP

Singapore

Asia

THA

Thailand

Eastern Europe

CYP

Cyprus

Eastern Europe

CZE

Czech Rep.

Eastern Europe

GRC

Greece

Eastern Europe

HRV

Croatia

Eastern Europe

HUN

Hungary

Eastern Europe

IRL

Ireland

Eastern Europe

LTU

Lithuania

Eastern Europe

LVA

Latvia

Eastern Europe

MLT

Malta

Eastern Europe

POL

Poland

Eastern Europe

PRT

Portugal

Eastern Europe

SVK

Slovakia

Eastern Europe

SVN

Slovenia

Eastern Europe

TUR

Turkey

Japan

JPN

Japan

Japan

KOR

Rep. of Korea

LatinAmerica

ARG

Argentina

LatinAmerica

BRA

Brazil

United States

USA

USA

Western Europe AUT

Austria

Western Europe BEL

Belgium

Western Europe CHE

Switzerland

61

Bloc

Country Code

Country Name

Western Europe DEU

Germany

Western Europe DNK

Denmark

Western Europe ESP

Spain

Western Europe FIN

Finland

Western Europe FRA

France

Western Europe GBR

United Kingdom

Western Europe ISL

Iceland

Western Europe ITA

Italy

Western Europe NLD

Netherlands

Western Europe NOR

Norway

Western Europe SWE

Sweden

62

14

Appendix C

The codes are under the classification of Broad Economic Categories (BEC). There are three basic classes of goods in SNA in the categories of BEC. These are as follows: 1. Capital goods Sum of categories: 41* Capital goods (except transport equipment) 521* Transport equipment, industrial 2. Intermediate goods Sum of categories: 111* Food and beverages, primary, mainly for industry 121* Food and beverages, processed, mainly for industry 21* Industrial supplies not elsewhere specified, primary 22* Industrial supplies not elsewhere specified, processed 31* Fuels and lubricants, primary 322* Fuels and lubricants, processed (other than motor spirit) 42* Parts and accessories of capital goods (except transport equipment) 53* Parts and accessories of transport equipment 3. Consumption goods Sum of categories: 112* Food and beverages, primary, mainly for household consumption 122* Food and beverages, processed, mainly for household consumption 522* Transport equipment, non-industrial 61* Consumer goods not elsewhere specified, durable 62* Consumer goods not elsewhere specified, semi-durable 63* Consumer goods not elsewhere specified, non-durable Table 15: Classification of goods according to BEC

63